Complete residue system

A Complete residue system modulo $n$ is a set of integers which satisfy the following condition: Every integer is congruent to a unique member of the set modulo $n$ .

In other words, the set contains exactly one member of each residue class.

Examples

$\{1,2,3\}$ , $\{4,5,6\}$ , and $\{9,17,85\}$ are all Complete residue systems $\pmod{3}$

$\{k,k+1,k+2,k+3,\ldots,k+m-1\}$ is a complete residue system $\pmod{m}$ , for any integer $k$ and positive integer $m$ . Basically, any consecutive string of $m$ integers forms a complete residue system $\pmod{m}$ .

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Complete residue system

Examples